EXHIBIT 32​

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

David P. Mansfield, President and Chief Executive Officer of Provident Bancorp, Inc. (the “Company”), and Carol L. Houle, Executive Vice President and Chief Financial Officer of the Company, each certify in his or her capacity as an officer of the Company that they have reviewed the annual report on Form 10-K for the year ended December 31, 2019 (the “Report”) and that to the best of their knowledge:

1.

the Report fully complies with the requirements of Sections 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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2.

the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

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A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.